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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maass wave form ： ウィキペディア英語版 Maass wave form In mathematics, a Maass wave form or Maass form is a function on the upper half plane that transforms like a modular form but need not be holomorphic. They were first studied by Hans Maass in . ==Definition== Let ''k'' be a half-integer, ''s'' be a complex number, and Γ be a discrete subgroup of SL2(R). A Maass form of weight ''k'' for Γ with Laplace eigenvalue ''s'' is a smooth function from the upper half-plane to the complex numbers satisfying the following conditions: *For all and all $\backslash tau\; \backslash in\; \backslash mathbb$, we have $f\backslash left(\backslash frac\backslash right)\; =\; (c\backslash tau+d)^k\; f(\backslash tau)$. *We have $\backslash Delta\_\; f\; =\; s\; f$, where $\backslash Delta\_$ is the weight ''k'' hyperbolic laplacian defined as $\backslash Delta\_\; =$ -y^ \left(\frac} + \frac}\right)+ i k y \left(\frac + i \frac\right). *The function ''f'' is of at most polynomial growth at cusps. A weak Maass wave form is defined similarly but with the third condition replaced by "The function ''f'' has at most linear exponential growth at cusps". Moreover, f is said to be harmonic if it is annihilated by the Laplacian operator. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maass wave form」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.